Edge congestion of shortest path systems for all-to-all communication

The problem of choosing a static shortest-path system that minimizes maximum edge congestion in a network is studied. Bounds based on parameters, such as diameter, bisection width, and average distance, are derived and conditions for producing uniform congestion on all edges are explored. Trees are shown to have maximum congestion on edges that are incident to a centroid node. Cartesian product graphs, which generalize multidimensional meshes, are shown to satisfy several closure properties and a generic factor-routing scheme is defined and shown to be optimal in many cases.